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Goal

I would like to figure out how to weight aggregated survey data to try to 'fix' the fact that a survey is not representative at the subnational level.

Background

I am attempting to aggregate survey data to the subnational level (Admin 1). I have data from a survey which is representative at the national level, but is not representative at the subnational level. When I aggregate data, some regions are represented by several hundred observations, whereas other regions are represented by only a dozen observations.

I would like to weight these aggregations so that each region is not over (or under) represented. I wouldn't want a region with 12 responses to be measured equally with a region with 140 responses.

My Solution

As far as I can figure, the best way to do this is to standardize the subnational means to the larger national mean, since I know that the survey is representative at the national level.

Here is what I came up with:

  1. I can acquire the aggregated mean of a given variable at the region-level ($\mu_{region}$)
  2. I can acquire the number of data points for each given variable at the region-level ($N_{region}$
  3. I can acquire the number of data points for each given variable at the country-level ($N_{country}$)

I would then weight each given aggregated mean by multiplying it against the ratio of the number of region data points to the number of country data points.

$$ Weighted.Variable = \mu_{region} * \frac{N_{region}}{N_{country}} $$

Question

Is this approach statistically appropriate for correcting for a lack of subnational representation?

I need a mind (or minds) greater than my own to figure out whether this is an appropriate transformation to apply to my data. If it is not, where should I look to solve this problem?

Thank you all so much for your help!

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  • $\begingroup$ So why do you think you need to reweight your analysis? $\endgroup$
    – StasK
    Aug 9, 2016 at 21:57

2 Answers 2

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No, this does not work. Instead of weighting the power of the variable, it simply affected the value of the variable.

So, in the end, this was a bad approach. I'll leave this up here in case there are any other people interested.

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First off, there is no concept of representative sample in serious sampling textbooks; this is mostly a folk-statistics concept. Second, if anything, the possibility to generalize the sample to the population (which is what I believe people usually mean by saying that their sample is "representative") lies in the design and in the sampling process, it has nothing to do with the sample size. So I am not surprised that your results are negative.

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